Have tried default route advertisement using 2 ways:

R1(config-if)#ip addr 192.168.1.1 255.255.255.0
R1(config-if)#router eigrp 123
R1(config-router)#net 192.168.1.0 0.0.0.255
R1(config-router)#exit

R1(config)#ip default-network 192.168.1.0

OR
R1(config)#ip route 0.0.0.0 0.0.0.0 FastEthernet1/0
R1(config)#router eigrp 123
R1(config-router)#net 0.0.0.0

But gateway of last resort for R4 is not set.

Also how do we make other routers prefer R1 over R2 ?

Do we use object tracking?

R4#sh ip route
Codes: L - local, C - connected, S - static, R - RIP, M - mobile, B - BGP
       D - EIGRP, EX - EIGRP external, O - OSPF, IA - OSPF inter area
       N1 - OSPF NSSA external type 1, N2 - OSPF NSSA external type 2
       E1 - OSPF external type 1, E2 - OSPF external type 2
       i - IS-IS, su - IS-IS summary, L1 - IS-IS level-1, L2 - IS-IS level-2
       ia - IS-IS inter area, * - candidate default, U - per-user static route
       o - ODR, P - periodic downloaded static route, + - replicated route

Gateway of last resort is not set

D*    192.168.1.0/24 [90/156160] via 123.45.67.5, 00:29:09, FastEthernet1/0